Differentiation and Integration Rules Flashcards
d/dx of cu
cu’
d/dx u +/- v
u’ +/- v’
d/dx uv
uv’ + vu’
d/dx u/v
vu’-uv’ all over v^2
d/dx c
0
d/dx u^n
n * u^n-1 * u’
d/dx x
1
d/dx |u|
u/|u| * u’ (u not equal to 0)
d/dx Ln u
1/u * u’
d/dx e^u
e^u * u’
d/dx logaU
1/Ln a * 1/u *u’
d/dx a^u
Ln a * a^u * u’
d/dx sin u
Cos u * u’
d/dx cos u
-sin u *u’
d/dx tan u
Sec^2 u *u’
d/dx Cot u
-Csc^2 u * u’
d/dx sec u
Sec u * tan u * u’
d/dx Csc u
-Csc u * cot u * u’
d/dx arcsin u
1/Square root of 1-u^2
Times u’
d/dx arccos u
-1/Square root of 1-u^2
Times u’
d/dx arctan u
1/1+u^2 * u’
d/dx arccot u
-1/1+u^2 * u’
d/dx arcsec u
1/absolute value of u * 1/Square root of u^2-1 *u’
d/dx arccsc u
-1/absolute value of u * 1/Square root of u^2-1 *u’
{k*f(u)
K{f(u)
{f(u)+/-g(u)
{f(u) +/- {g(u)
{du
U + C
{u^n
1/n+1 * u^n+1 + C (n not equal to -1)
{du/u
Ln |u| + C
{e^u du
E^u + C
{a^u de
1/Ln a * a^u + C
{sin u du
-cos u + C
{cos u du
Sin u + C
{tan u du
-ln|cos u| + C
{cot u du
Ln|sin u| + C
{sec u du
Ln|sec u + tan u| + C
{csc u du
-ln|csc u + cot u| +C
{du/Square root of a^2-u^2
Arc sin u/a + C
{du/a^2+u^2
1/a arctan u/a + C
{du/u*Square root of u^2-a^2
1/a arcsec |u|/a + C
{Sec^2 u du
Tan u + C
{Csc^2 u du
-Cot u +C
{Sec u * tan u du
Sec u + C
{Csc u * cot u du
-Csc u + C
{Y’=ky
Y=Ce^kx
{Y’=ky(1-y/L)
Y=L/(1+be^-kt)
The integration of udv
U*V minus the integration of vdu
